Wet gas measurement

ABSTRACT

A first apparent property of a multi-phase process fluid is determined based on the motion of the vibratable flowtube. One or more apparent intermediate values associated with the multi-phase process fluid are determined based on the first apparent property. A measure of wetness of the multi-phase process fluid is determined based on a mapping between one or more of the apparent intermediate values and the measure of wetness. A second apparent property of the multi-phase process fluid is determined using the differential pressure flowmeter. One or more phase-specific properties of the multi-phase process fluid is determined based on the measure of wetness and the second apparent property.

This application claims priority to U.S. Provisional Application Ser.No. 60/913,148, titled WET GAS CALCULATIONS, and filed on Apr. 20, 2007,and U.S. Provisional Application Ser. No. 60/977,531 titled WET GASMEASUREMENT, and filed on Oct. 4, 2007, both of which are incorporatedby reference.

TECHNICAL FIELD

This description relates to flowmeters.

BACKGROUND

Flowmeters provide information about materials being transferred througha conduit. For example, mass flowmeters provide a measurement of themass of material being transferred through a conduit. Similarly,densitometers provide a measurement of the density of material flowingthrough a conduit. Mass flowmeters also may provide a measurement of thedensity of the material.

For example, Coriolis-type mass flowmeters are based on the Corioliseffect, in which material flowing through a conduit becomes aradially-travelling mass that is affected by a Coriolis force andtherefore experiences an acceleration. Many Coriolis-type massflowmeters induce a Coriolis force by sinusoidally oscillating a conduitabout a pivot axis orthogonal to the length of the conduit. In such massflowmeters, the Coriolis reaction force experienced by the travelingfluid mass is transferred to the conduit itself and is manifested as adeflection or offset of the conduit in the direction of the Coriolisforce vector in the plane of rotation.

SUMMARY

In one general aspect, a multi-phase process fluid is passed through avibratable flowtube and a differential pressure flowmeter, and motion isinduced in the vibratable flowtube. A first apparent property of themulti-phase process fluid is determined based on the motion of thevibratable flowtube. One or more apparent intermediate values associatedwith the multi-phase process fluid are determined based on the firstapparent property. A measure of wetness of the multi-phase process fluidis determined based on a mapping between one or more of the apparentintermediate values and the measure of wetness. A second apparentproperty of the multi-phase process fluid is determined using thedifferential pressure flowmeter. One or more phase-specific propertiesof the multi-phase process fluid are determined based on the measure ofwetness and the second apparent property.

Implementations may include one or more of the following features.Determining one or more apparent intermediate values associated with themulti-phase process fluid based on the first apparent property mayinclude determining a first Froude number corresponding to a non-gasphase of the multi-phase process fluid and a second Froude numbercorresponding to a gas phase of the multi-phase process fluid.Determining the measure of wetness of the multi-phase process fluidbased on a mapping between one or more of the apparent intermediatevalues and the measure of wetness may include determining the measure ofwetness of the multi-phase process fluid based on a mapping between thefirst and second Froude numbers and the measure of wetness.

The multi-phase process fluid may be a wet gas. The first apparentproperty may be an apparent mass flow rate. The measure of wetness maybe a Lockhart-Martinelli parameter. The differential pressure flowmetermay be an orifice plate. The second apparent property may be a mass flowrate of the multi-phase process fluid as a dry gas.

One or more corrected intermediate values may be determined based on amapping between one or more of the apparent intermediate values and thecorrected intermediate values. One or more phase-specific properties ofthe multi-phase fluid may be determined based on the correctedintermediate values. The phase-specific properties of the phase of themulti-phase fluid determined based on the corrected intermediate valuemay be compared to the phase-specific properties of the multi-phaseprocess fluid determined based on the measure of wetness and the secondapparent property.

Determining one or more phase-specific properties of the multi-phaseprocess fluid based on the measure of wetness and the second apparentproperty may include determining a mass flow rate of a gas phase of themulti-phase process fluid. The mapping is a neural network.

Implementations of any of the techniques described above may include amethod or process, a system, a flowmeter, or instructions stored on astorage device of flowmeter transmitter. The details of particularimplementations are set forth in the accompanying drawings anddescription below. Other features will be apparent from the followingdescription, including the drawings, and the claims.

DESCRIPTION OF DRAWINGS

FIG. 1A is an illustration of a Coriolis flowmeter using a bentflowtube.

FIG. 1B is an illustration of a Coriolis flowmeter using a straightflowtube.

FIG. 2 is a block diagram of a Coriolis flowmeter.

FIG. 3 is a block diagram showing a system that includes a differentialpressure flowmeter and a Coriolis flowmeter.

FIG. 4 is a block diagram of a digital controller implementing a neuralnetwork processor that may be used with the digital mass flowmeter formultiple-phase fluid flows.

FIGS. 5A and 5B are flowcharts illustrating a process that employs aCoriolis flowmeter and a differential pressure flowmeter for multi-phasefluids.

FIG. 6 is a flowchart illustrating a process for using a Coriolis meterand a differential pressure flowmeter.

FIG. 7 is an illustration of jacketing.

DETAILED DESCRIPTION

Types of flowmeters include digital Coriolis flowmeters. For example,U.S. Pat. No. 6,311,136, which is hereby incorporated by reference,discloses the use of a digital Coriolis flowmeter and related technologyincluding signal processing and measurement techniques. Such digitalflowmeters may be very precise in their measurements, with little ornegligible noise, and may be capable of enabling a wide range ofpositive and negative gains at the driver circuitry for driving theconduit. Such digital Coriolis flowmeters are thus advantageous in avariety of settings. For example, commonly-assigned U.S. Pat. No.6,505,519, which is incorporated by reference, discloses the use of awide gain range, and/or the use of negative gain, to prevent stallingand to more accurately exercise control of the flowtube, even duringdifficult conditions such as two-phase flow (e.g., a flow containing amixture of liquid and gas).

Although digital Coriolis flowmeters are specifically discussed belowwith respect to, for example, FIGS. 1A, 1B and 2, it should beunderstood that analog Coriolis flowmeters also exist. Although suchanalog Coriolis flowmeters may be prone to typical shortcomings ofanalog circuitry, e.g., low precision and high noise measurementsrelative to digital Coriolis flowmeters, they also may be compatiblewith the various techniques and implementations discussed herein. Thus,in the following discussion, the term “Coriolis flowmeter” or “Coriolismeter” is used to refer to any type of device and/or system in which theCoriolis effect is used to measure a mass flowrate, density, and/orother parameters of a material(s) moving through a flowtube or otherconduit.

FIG. 1A is an illustration of a digital Coriolis flowmeter using a bentflowtube 102. Specifically, the bent flowtube 102 may be used to measureone or more physical characteristics of, for example, a (travelling ornon-travelling) fluid, as referred to above. In FIG. 1A, a digitaltransmitter 104 exchanges sensor and drive signals with the bentflowtube 102, so as to both sense an oscillation of the bent flowtube102, and to drive the oscillation of the bent flowtube 102 accordingly.By quickly and accurately determining the sensor and drive signals, thedigital transmitter 104, as referred to above, may provide for fast andaccurate operation of the bent flowtube 102. Examples of the digitaltransmitter 104 being used with a bent flowtube are provided in, forexample, commonly-assigned U.S. Pat. No. 6,311,136.

FIG. 1B is an illustration of a digital Coriolis flowmeter using astraight flowtube 106. More specifically, in FIG. 1B, the straightflowtube 106 interacts with the digital transmitter 104. Such a straightflowtube operates similarly to the bent flowtube 102 on a conceptuallevel, and has various advantages/disadvantages relative to the bentflowtube 102. For example, the straight flowtube 106 may be easier to(completely) fill and empty than the bent flowtube 102, simply due tothe geometry of its construction. In operation, the bent flowtube 102may operate at a frequency of, for example, 50-110 Hz, while thestraight flowtube 106 may operate at a frequency of, for example,300-1,000 Hz. The bent flowtube 102 represents flowtubes having avariety of diameters, and may be operated in multiple orientations, suchas, for example, in a vertical or horizontal orientation. The straightflowtube 106 also may have a variety of diameters, and may be operatedin multiple orientations.

Referring to FIG. 2, a digital mass flowmeter 200 includes the digitaltransmitter 104, one or more motion sensors 205, one or more drivers210, a flowtube 215 (which also may be referred to as a conduit, andwhich may represent either the bent flowtube 102, the straight flowtube106, or some other type of flowtube), a temperature sensor 220, and apressure sensor 225. The digital transmitter 104 may be implementedusing one or more of, for example, a processor, a Digital SignalProcessor (DSP), a field-programmable gate array (FPGA), an ASIC, otherprogrammable logic or gate arrays, or programmable logic with aprocessor core. It should be understood that, as described in U.S. Pat.No. 6,311,136, associated digital-to-analog converters may be includedfor operation of the drivers 210, while analog-to-digital converters maybe used to convert sensor signals from the sensors 205 for use by thedigital transmitter 104.

The digital transmitter 104 may include a bulk density measurementsystem 240 and a bulk mass flowrate measurement system 250. Bulkproperties generally refer to properties of the fluid as a whole, asopposed to the properties of a constituent component of the fluid whenmulti-phase flow is present (as described below). Density measurementsystem 240 and mass flowrate measurement system 250 may generatemeasurements of, respectively, density and/or mass flowrate of amaterial flowing through the flowtube 215 based at least on signalsreceived from the motion sensors 205. The digital transmitter 104 alsocontrols the drivers 210 to induce motion in the flowtube 215. Thismotion is sensed by the motion sensors 205.

Density measurements of the material flowing through the flowtube arerelated to, for example, the frequency of the motion of the flowtube 215that is induced in the flowtube 215 (typically the resonant frequency)by a driving force supplied by the drivers 210, and/or to thetemperature of the flowtube 215. Similarly, mass flow through theflowtube 215 is related to the phase and frequency of the motion of theflowtube 215, as well as to the temperature of the flowtube 215.

The temperature in the flowtube 215, which is measured using thetemperature sensor 220, affects certain properties of the flowtube, suchas its stiffness and dimensions. The digital transmitter 104 maycompensate for these temperature effects. Also in FIG. 2, a pressuresensor 225 is in communication with the transmitter 104, and isconnected to the flowtube 215 so as to be operable to sense a pressureof a material flowing through the flowtube 215.

It should be understood that both the pressure of the fluid entering theflowtube 215 and the pressure drop across relevant points on theflowtube may be indicators of certain flow conditions. Also, whileexternal temperature sensors may be used to measure the fluidtemperature, such sensors may be used in addition to an internalflowmeter sensor designed to measure a representative temperature forflowtube calibrations. Also, some flowtubes use multiple temperaturesensors for the purpose of correcting measurements for an effect ofdifferential temperature between the process fluid and the environment(e.g., a case temperature of a housing of the flowtube).

In FIG. 2, it should be understood that the various components of thedigital transmitter 104 are in communication with one another, althoughcommunication links are not explicitly illustrated, for the sake ofclarity. Further, it should be understood that conventional componentsof the digital transmitter 104 are not illustrated in FIG. 2, but areassumed to exist within, or be accessible to, the digital transmitter104. For example, the digital transmitter 104 will typically includedrive circuitry for driving the driver 210, and measurement circuitry tomeasure the oscillation frequency of the flowtube 215 based on sensorsignals from sensors 205 and to measure the phase between the sensorsignals from sensors 205.

Under certain conditions, a Coriolis flowmeter can accurately determinethe bulk density and bulk mass flowrate of a process fluid in theflowtube 215. That is, an accurate bulk density and/or bulk massflowrate of the process fluid can be determined under certainconditions.

Also, in some situations, the process fluid may contain more than onephase by being a mixture of two or more materials (for example, oil andwater or a fluid with entrained gas), by being the same material indifferent phases (for example, liquid water and water vapor), or bybeing different materials in different phases (for example, water vaporand oil). In some multi-phase flow conditions, a Coriolis flowmeter mayaccurately determine the bulk density and bulk mass flowrate of thefluid, which can then be used to accurately determine the density and/ormass flowrate of the constituent phases.

Under other multi-phase flow conditions, however, a Coriolis flowmetermay not perform in a satisfactory manner. Although the Coriolisflowmeter continues to operate in the presence of the multi-phaseprocess fluid, the presence of the multi-phase fluid affects the motionof the flowtube (or conduit) that is part of the Coriolis flowmeter.Thus, the outputs determined by the meter may be inaccurate because themeter operates on the assumption that the process fluid is either singlephase, or the process fluid is a multi-phase fluid with properties suchas high liquid viscosity and/or no slip between phases. These outputsmay be referred to as apparent properties because they have not beencorrected for the effects of multi-phase flow. While apparent propertiesgenerally are those that have not been corrected for the effects ofmulti-phase flow, initial estimates of these properties may have beencorrected for other effects to generate the apparent properties. Forinstance, initial estimates of these properties may be corrected for theeffects of temperature and/or pressure on the properties to generate theapparent properties.

For instance, under some multi-phase flow conditions, a Coriolisflowmeter may not be able to measure the bulk density, the bulk massflowrate, the density of constituent components of a multi-phase flow,or the mass flowrates of constituent components of a multi-phase flowwithin the required tolerances needed in a particular applicationbecause these properties are determined based on an assumption thatsingle-phase flow is present, and the resulting errors introduced bymulti-phase flow are greater than the required tolerances. In otherwords, the Coriolis flowmeter may not be able to measure such itemswithin the requisite degree of accuracy for a given use of the Coriolisflowmeter.

Examples of such conditions include situations in which the processfluid is a wet gas (that is, it contains mostly a gas component, but hassome liquid component). A wet gas typically occurs in applicationsinvolving natural gas, where the gas component is the natural gas, andthe liquid component may be water, hydrocarbons, or compressor oil (orsome combination thereof). Other applications in which a wet gas occursmay include applications involving steam as the process fluid.

A wet gas generally includes a process fluid that contains 5% by volumeor less of a liquid or, in other words, a process fluid that has a voidfraction of 0.95 (95%) or more. However, the techniques described belowwith respect to wet gasses are not limited to process fluids thatcontain 5% by volume of less or a liquid. Rather, the techniques arebounded by the required accuracy of a given application, with theaccuracy depending on the accuracy of the Coriolis flowmeter and othermeters described below for a given void fraction.

Referring to FIG. 3, a differential pressure flowmeter 304 may be usedin combination with a Coriolis flowmeter 306 to more accurately measurethe properties of a wet gas or other multi-phase process fluid. Asillustrated, a system 300 includes a conduit 302 that carries theprocess fluid (e.g., wet gas), a differential pressure flowmeter 304, aCoriolis flowmeter 306 that measures the apparent bulk mass flowrate andapparent bulk density of the process fluid, and a flow computer 308. Insome implementations, the flow computer 308 may act as the transmitter104 discussed above. In some implementations, the flow computer 308 maybe separate from the differential pressure flowmeter 304 and theCoriolis flowmeter 306. In general, differential pressure flowmeters,such as the differential pressure flowmeter 304, guide the flow of aprocess fluid into a section of the differential pressure flowmeter 304that has a cross sectional area different than the cross sectional areaof the conduit that carries the process fluid. This results invariations of the flow velocity and the pressure. By measuring thechanges in pressure, the flow velocity can be calculated. The bulk massflowrate can be calculated from the flow velocity. However, as with theCoriolis flowmeter, the calculations of bulk mass flowrate may beperformed based on an assumption of single-phase flow, and therefore themeasurement may be inaccurate when a multi-phase fluid is present.Hence, the bulk mass flowrate may be an apparent bulk mass flowratebecause it has not been corrected to account for multi-phase flow.

In some implementations, the differential pressure flowmeter 304 may bean orifice plate. An orifice plate is typically a flat plate thatincludes an orifice. An orifice plate is normally mounted between a pairof flanges and installed in a straight run of smooth pipe to avoiddisturbance of flow patterns from fittings and valves.

Flow through an orifice plate is characterized by a change in velocity.As the fluid passes through the orifice, the fluid converges, and thevelocity of the fluid increases to a maximum value. At this point, thepressure is at a minimum value. As the fluid diverges to fill the entirepipe area, the velocity decreases back to the original value. Thepressure increases towards the original input value, typicallyrecovering 60-80% of the maximum pressure drop. The pressures on bothsides of the orifice are measured, resulting in a differential pressure,which is proportional to the flow velocity. From the velocity and thedensity of the fluid, the apparent bulk mass flowrate can be calculatedfor a known fluid density.

Thus, the differential pressure flowmeter 304 may be an orifice plate.The orifice plate may include the conduit 302 for carrying the processfluid and an orifice plate located in the conduit 302. An arrow 310illustrates the direction of flow. Upstream from the orifice plate is afirst pressure sensor and downstream from the orifice plate is a secondpressure sensor. The difference between the measurements of the firstsensor and the second sensor provides the differential pressure, whichmay be used to calculate the flow velocity and the apparent bulk massflowrate.

The apparent bulk properties determine by the Coriolis flowmeter 306 andthe differential pressure flowmeter 304 may be used to determinecorrected values of, e.g., the mass flowrates of the constituentcomponents of the fluid, as described further below.

To that end, and with reference to FIG. 4, Coriolis flowmeter 306 mayuse a digital controller 400 in place of the digital transmitter 104described above with respect to FIGS. 1A, 1B, and 2. The digitalcontroller 400 also may be referred to as a digital transmitter. In thisimplementation of the digital transmitter 104, process sensors 404connected to the flowtube generate process signals including one or moresensor signals, one or more temperature signals, and one or morepressure signals. For example, the process sensors 404 may include thetemperature sensor 220, the pressure sensor 225, and/or the motionsensors 205 described with respect to FIG. 2. The analog process signalsare converted to digital signal data by A/D converters 406 and stored insensor and driver signal data memory buffers 408 for use by the digitalcontroller 400. The drivers 445 connected to the flowtube generate adrive current signal and may communicate this signal to the A/Dconverters 406. The drive current signal then is converted to digitaldata and stored in the sensor and driver signal data memory buffers 408.Generally, it is assumed that the digital drive signal generated by theA/D converters 406 produces a digital drive signal corresponding to theanalog drive signal. In some implementations, the digital drive signalmay be monitored to ensure that the digital drive signal has theappropriate amplitude, phase, and frequency characteristics (e.g., thatthe digital drive signal is an accurate representation of the analogdrive signal). The drive voltage also may be monitored. The monitoringmay be accomplished by an additional A/D channel. The data sampled bythe additional AID channel may be analyzed in a manner similar to thatof the sensor data. This sampled data may be used for diagnosticpurposes as well as for maintaining. Alternatively, a digital drive gainsignal and a digital drive current signal may be generated by theamplitude control module 435 and communicated to the sensor and driversignal data memory buffers 408 for storage and use by the digitalcontroller 400.

The digital process sensor and driver signal data are further analyzedand processed by a sensor and driver parameters processing module 410that generates physical parameters including frequency, phase, current,damping and amplitude of oscillation. This information is provided to araw bulk mass flow measurement module 412 and a raw bulk densitymeasurement module 414. The raw mass flow measurement module 412generates a raw bulk mass-flowrate measurement signal that indicates theapparent bulk mass flowrate of the fluid. The raw bulk densitymeasurement module 414 generates a raw bulk density measurement signalthat indicates the apparent bulk density of the fluid.

A multiple-phase flow error correction module 420 receives, as input,the physical parameters from the sensor and driver parameters processingmodule 410, the raw bulk mass flowrate measurement signal, and the rawbulk density measurement 414. When the process fluid may contain asingle-phase or multi-phase flow condition, a flow condition state maybe detected, which causes the processing by the multiple-phase flowerror correction module 420 when multi-phase flow is present, or skipsprocessing by the multiple-phase flow error correction module 420 whensingle phase flow is present. However, if the process fluid involves aknown two-phase (e.g., gas and liquid constituents), three-phase (e.g.,gas and two-liquid constituents) or other multiple-phase flow (e.g., oneor more gas and one or more liquid constituents), the determination of aflow condition state may not be necessary. In this example, the processfluid may be a wet-gas that is already known to include a gas volumefraction (gvf) and liquid volume fraction (lvf).

The multiple-phase flow error correction module 420 includes one or moremapping functions such as a neural network that is used to helpcompensate for multi-phase flow conditions. The mapping functions can beimplemented in a software routine, or alternatively may be implementedas a separate programmed hardware processor.

The inputs to one of the mapping functions may be apparent intermediatevalues determined from the apparent bulk mass flowrate measurementsignal and the apparent bulk density measurement signal. In thisimplementation, the multiple-phase flow error correction module 420determines apparent intermediate values from the raw bulk mass flowrateand apparent bulk density of the multi-phase process fluid. The apparentintermediate values are input into the mapping function, which producesa measure of wetness (e.g., a Lockhart-Martinelli parameter, X_(L-M)) asan output. The multiple-phase flow error correction module 420 may thenoutput 422 the measure of wetness X_(L-M).

A second mapping function may also input apparent intermediate valuesdetermined from the apparent bulk mass flowrate measurement signal andthe apparent bulk density measurement signal. In this implementation,the multiple-phase flow error correction module 420 determines apparentintermediate values from the raw bulk mass flowrate and apparent bulkdensity of the multi-phase process fluid. The apparent intermediatevalues input to the second mapping function may be the same as ordifferent than the apparent intermediate values input to the firstmapping function. The apparent intermediate values are input into thesecond mapping function and corrected for the effects of multi-phaseflow. The corrected apparent intermediate values are output to amass-flow measurement output block 430. In other implementations, theapparent (or raw) bulk mass-flow measurement and apparent bulk densitymay be input to one or both of the mapping functions.

When a neural network is used, a neural network coefficients andtraining module 425 stores a predetermined set or sets of neural networkcoefficients that are used by the neural network processor for thecorrection described above. The neural network coefficients and trainingmodule 425 also may perform an online training function using trainingdata so that an updated set of coefficients can be calculated for use bythe neural network. While the predetermined set of neural networkcoefficients are generated through extensive laboratory testing andexperiments based upon known two-phase, three-phase, or higher-phasemass-flowrates, the online training function performed by module 425 mayoccur at the initial commissioning stage of the flowmeter, or may occureach time the flowmeter is initialized.

As indicated above, the multiple-phase flow error correction module 420may output 422 the measure of wetness X_(L-M). The measure of wetness isthen used with measurements made by the differential pressure flowmeter304 to determine accurate or corrected measurements of phase-specificproperties of the fluid, such as the mass flowrate of the constituentphases, as described further below.

Also, the corrected intermediate values from the mapping function areinput to the mass-flow measurement output block 430. Using the correctedintermediate values, the mass-flow measurement output block 430determines estimates of phase-specific properties of the fluid, such asthe mass flowrates of the constituent phases of the multi-phase fluid.When the estimated phase-specific properties and the correctedphase-specific properties are both the mass flowrates of the constituentcomponents of the multi-phase fluid, the estimates may be compared tothe corrected measurements of phase-specific properties of the fluid todetermine whether the differential pressure flowmeter 304 and Coriolisflowmeter 306 are functioning properly.

The sensor parameters processing module 410 also inputs a dampingparameter and an amplitude of oscillation parameter to an amplitudecontrol module 435. The amplitude control module 435 further processesthe damping parameter and the amplitude of oscillation parameter andgenerates digital drive signals. The digital drive signals are convertedto analog drive signals by D/A converters 440 for operating the drivers445 connected to the flowtube of the digital flowmeter. In someimplementations, the amplitude control module 435 may process thedamping parameter and the amplitude of oscillation parameter andgenerate analog drive signals for operating the drivers 445 directly.

Referring to FIGS. 5A and 5B, example processes 500A and 500B may beimplemented by system 300 and controller 400 to determine a correctedphase-specific property of a phase included in a multi-phase processfluid. For example, the processes 500A and 500B may be used to determinethe mass flowrate of each phase of the multi-phase process fluid. Themulti-phase process fluid may be, for example, a three-phase fluid suchas a wet gas that includes a gas phase and two liquid phases (e.g.,methane, water, and oil).

As described below, in one implementation, one or more apparentintermediate values are determined based on apparent or raw propertiesof the multi-phase fluid. For example, an apparent intermediate valuemay be determined based on an apparent bulk mass flowrate and/or anapparent bulk density of the multi-phase process fluid as determined by,for example, Coriolis flowmeter 306. The apparent intermediate value isinput into, e.g., a neural network to produce a measure of wetness ofthe multi-phase process fluid. Using an intermediate value rather thanthe apparent bulk mass flowrate and apparent bulk density of themulti-phase process fluid may help improve the accuracy of thedetermination of the measure of wetness. The measure of wetness is thenused with measurements from the differential pressure flowmeter (e.g.,orifice plate) to determine corrected values of phase-specificproperties of the multi-phase fluid, such as the mass flowrates of thephases of the multi-phase fluid.

A multi-phase process fluid is passed through a vibratable flowtube(505) and motion is induced in the vibratable flowtube (510). Thevibratable flowtube maybe, for example, the flowtube 215 described withrespect to FIG. 2. The multi-phase process fluid may be a two-phasefluid, a three-phase fluid, or a fluid that includes more than threephases. For example, a two-phase fluid may include a non-gas phase,which may be a liquid such as oil, and a gas phase, such as methane. Athree-phase fluid may include a gas phase and two non-gas phases. Thetwo non-gas phases may be liquids (such as oil and water), or the twonon-gas phases may be a liquid phase (such as oil) and a solid phase(such as sand). The multi-phase fluid may be a wet gas. While the wetgas may be any of the multi-phase fluids described above, in general, awet gas is composed of more than 95% gas phase by volume. In generaleach phase of the multi-phase fluid may be referred to as constituentsor components of the multi-phase fluid. The processes 500A and 500B maybe applied to any multi-phase fluid.

A first apparent property of the multi-phase fluid is determined basedon the motion of the vibratable flowtube (515). The first apparentproperty of the multi-phase fluid maybe the apparent bulk mass flowrateand/or the apparent bulk density of the fluid flowing through thevibratable flowtube. As described above, an apparent property is onethat has not been corrected for the effects the multi-phase fluid has onthe motion of the flowtube. However, such properties may have beencorrected for other effects to generate the apparent properties. Forinstance, initial estimates of these properties may be corrected for theeffects of temperature and/or pressure on the properties to generate theapparent properties.

In general, additional information (e.g., the known densities of thematerials in the individual phases) and/or additional measurements(e.g., pressure of the multi-phase fluid or the water-cut of themulti-phase fluid) may be used at times. Thus, in some implementations,in addition to properties determined based on the motion of the conduit,such as the first apparent property discussed above, additional or“external” properties of the multi-phase fluid such as temperature,pressure, and water-cut may be measured and used, e.g., as additionalinputs to the mapping described below, to determine one or more apparentintermediate values as described below, or to help in determining theflowrates of the individual components of the multi-phase fluid. Theadditional properties may be measured by a device other than theflowmeter. For example, the water-cut of the multi-phase fluid, whichrepresents the portion of the multi-phase fluid that is water, may bedetermined by a water-cut meter. The additional property also mayinclude a pressure associated with the flowtube. The pressure associatedwith the flowtube may be, for example, a pressure of the multi-phaseprocess fluid at an inlet of the flowtube and/or a differential pressureacross the flowtube. The additional property may be the temperature ofthe multi-phase process fluid.

In some implementations, more than one apparent property may bedetermined based on the motion of the conduit. For example, in such animplementation, the apparent bulk mass flowrate of the multi-phase fluidand the apparent bulk density of the multi-phase fluid may be determinedbased on the motion of the conduit, and both of these apparentproperties may be used to determine one or more apparent, intermediatevalues (such as a gas and a liquid Froude number, as described below).The following describes examples of how the apparent bulk mass flowrateand apparent bulk density can be determined.

The apparent bulk mass flowrate may be determined from the average ofthe apparent mass flowrate determined from the Coriolis meter, where theperiod of averaging is selected to represent a balancing between noisereduction due to two-phase effects on the one hand, and maintaining adynamic response to genuine changes in the flowrate on the other. Theaveraging period may be, for example, 1 second. The following equationexpresses the relationship between the average apparent mass flowrateand the apparent bulk mass flowrate:

m_(m) ^(a)= m _(o).

The apparent mass flowrate from the Coriolis meter may be determinedfrom the following equation, where φ is the observed phase angledifference of the flowtube 215 in degrees measured by the sensors 205(e.g., the phase difference between signals measured by the sensors205), f is the observed frequency of the flowtube 215 in Hertz, T is thetemperature of the flowtube 215 in degrees Celsius, A and B areflowtube-type specific temperature coefficients, F₂ is a flowcalibration factor, and F_(f) is a field-adjustable flowfactor (whichhas a nominal value of 1.000):

T₀ = 20^(∘)  C.Δ T = T − T₀$m_{0} = {F_{f} \cdot F_{2} \cdot \left( {1 + {{A \cdot \Delta}\; T} + {{B \cdot \Delta}\; T^{2}}} \right) \cdot \frac{6400}{f} \cdot {{\tan \left( {\frac{\pi}{360}\varphi} \right)}.}}$

The apparent bulk density of the multi-phase process fluid may bedetermined from the average of the apparent density determined from theCoriolis meter:

${\rho_{m}^{a} = {\overset{\_}{\rho}}_{p}},{where}$T₀ = 20.0^(∘)  C.Δ T = T − T₀ Δ P = P_(i) − P₀$\rho_{0} = {{\frac{256}{f^{2}} \cdot D_{2} \cdot \left( {1 + {{C \cdot \Delta}\; T}} \right)} + {D_{4} \cdot \left( {1 + {{D \cdot \Delta}\; T}} \right)}}$ρ_(p) = ρ₀ + k_(pd) ⋅ (P_(i) − P₀) + k_(dbias).

In the above equation, ρ₀ is the raw density in kg/m³, ρ_(p) is thepressure corrected density in kg/m³, P_(i) barA is the inlet pressure ofthe flowtube 215, P₀ barA is a configured reference pressure, k_(pd)kg/m³/bar and k_(dbias) kg/m³ are flowtube specific calibrationconstants valid for specific flowtube operating pressure and gas densityranges, f is the natural frequency of the flowtube 215 in Hertz, P₀ is areference pressure in barA, P_(i) is the inlet pressure in barA, and Tis the temperature of the flowtube in degrees Celsius, D₂ and D₄ areflowtube-specific calibration constants. C and D are flowtube-typespecific temperature compensation parameters. A more general equation tocorrect the apparent bulk density for pressure is as follows, wherek_(pd2) and k_(pd4) are flowtube-specific calibration constants:

T₀ = 20.0^(∘)  C.Δ T = T − T₀ Δ P = P_(i) − P₀$\rho_{p} = {{\frac{256}{f^{2}} \cdot D_{2} \cdot \left( {1 + {{C \cdot \Delta}\; T}} \right) \cdot \left( {1 + {k_{{pd}\; 2}\Delta \; P}} \right)} + {D_{4} \cdot \left( {1 + {{D \cdot \Delta}\; T}} \right) \cdot {\left( {1 + {k_{{pd}\; 4}\Delta \; P}} \right).}}}$

One or more apparent intermediate values associated with the multi-phaseprocess fluid are determined based on the first apparent property (520).In general, the apparent intermediate value (or values) is a valuerelated to the multi-phase fluid that includes inaccuracies resultingfrom the inclusion of more than one phase in the multi-phase fluid. Theapparent intermediate value may be, for example, a gas or a non-gasFroude number.

In one implementation, the apparent intermediate values may include bothan apparent non-gas Froude number and an apparent gas Froude number.Froude numbers are dimensionless quantities that may represent aresistance of an object moving through a fluid and that may be used tocharacterize multi-phase fluids. The apparent gas Froude number may becalculated using the following equation, where m_(g) ^(a) is theapparent gas mass flow rate, ρ_(g) is an estimate of the density of thegas phase based on the ideal gas laws (or any model of true gas density,such as, for example, American Gas Association (AGA) or InternationalStandards Organization (ISO) standards, using knowledge of the componentmaterials and observed pressure and temperature), ρ_(i) is an estimateof the density of the liquid in the non-gas phase of the multi-phasefluid, A is the cross-sectional area of the flowtube, D is the diameterof the flowtube, and g is the acceleration due to gravity:

${Fr}_{g}^{a} = {{\frac{m_{g}^{a}}{\rho_{g}A\sqrt{g \cdot D}}\sqrt{\frac{\rho_{g}}{\rho_{l} - \rho_{g}}}} = {K \cdot V_{g}^{a} \cdot \sqrt{\frac{\rho_{g}}{\rho_{l} - \rho_{g}}}}}$${{{where}\mspace{14mu} K} = \frac{1}{\sqrt{g \cdot D}}},{{{the}\mspace{14mu} {Apparent}\mspace{14mu} {Gas}\mspace{14mu} {Velocity}\mspace{14mu} V_{g}^{a}} = {\frac{m_{g}^{a}}{\rho_{g}A}.}}$

Similarly, the non-gas Froude number (which may be a liquid Froudenumber) may be calculated using the following equation, where m_(l) ^(a)is the apparent liquid mass flow rate mass flowrate of the liquidmixture if more than one liquid is present):

${Fr}_{l}^{a} = {{\frac{m_{l}^{a}}{\rho_{l}A\sqrt{g \cdot D}}\sqrt{\frac{\rho_{l}}{\rho_{l} - \rho_{g}}}} = {K \cdot V_{l}^{a} \cdot {\sqrt{\frac{\rho_{l}}{\rho_{l} - \rho_{g}}}.}}}$

The estimates of the densities of the liquid and gas phases of themulti-phase fluid may be determined as discussed below. In this example,the multi-phase fluid includes two liquid phases (for example, a firstliquid that is water and a second liquid that is a condensate) and a gasphase. However, similar calculations may be performed for othermulti-phase fluids. In the equations below, ρ_(l0) kg/m³ is the baseliquid density at a known temperature, T_(l0)° C., and k_(l)/° C. is acoefficient that provides a linear correction to this density as afunction of temperature difference from the base temperature T_(l0), areknown from knowledge of the particular substances that are included inthe multi-phase fluid. The component fluid densities ρ_(l1), ρ_(l2)kg/m³ at the current fluid temperature may be determined by:

ρ_(l1)=ρ_(l10)·(1+k _(l1)·(T−T _(l10))).

ρ_(l2)=ρ_(l20)·(1+k _(l2)·(T−T _(l20))).

In some implementations, the user may input the volumetric flow fraction(x) of the first liquid. In other implementations, the volumetric flowfraction may be assumed. In still other implementations, the volumetricflow fraction may be estimated, or obtained from a water-cut measuringdevice such as a water-cut meter.

Assuming no slip between liquid phases, the volumetric flow fraction ofthe first liquid x₁ % may be determined by:

$x_{1} = {{\left( \frac{\rho_{l} - \rho_{l\; 2}}{\rho_{l\; 1} - \rho_{l\; 2}} \right) \cdot 100}{\%.}}$

Using x₁ %, and assuming no slip between liquid phases, the combinedliquid density (i.e., liquid density of the liquid mixture) may becalculated with:

$\rho_{l} = {\rho_{l\; 2} + {\frac{x_{1}}{100} \cdot \left( {\rho_{l\; 1} - \rho_{l\; 2}} \right)}}$or$\rho_{l} = {{\frac{x_{1}}{100} \cdot \rho_{l\; 1}} + {\left( {1 - \frac{x_{1}}{100}} \right){\rho_{l\; 2}.}}}$

Additionally, an estimate of the gas density ρ_(g) kg/m³ at lineconditions of pressure P₁ barA and T_(i)° C. at the inlet the Coriolisflowtube may be determined given a reference density of the gas ρ_(g0)kg/m³ at a reference pressure P_(g0) barA and reference temperatureT_(g0)° C. While there are a number of equations of state that take intoaccount compressibility and other non-idealities, the estimate of theactual gas density using the ideal gas laws is assumed to be sufficientand the density of the gas phase may be estimated based on:

$\rho_{g} = {\rho_{g\; 0} \cdot \frac{P_{i}}{P_{g\; 0}} \cdot \left( \frac{T_{g\; 0} + 273.15}{T_{i} + 273.15} \right) \cdot {\left( \frac{1}{Z_{f}} \right).}}$

In the above equation, Z_(f) is the compressibility of the gas in thegas phase, and for some gases (such as natural gas), the compressibilityvaries with pressure according to the following equation:

Z _(f) =Z _(f0) +k _(zp)·(P−P ₀).

The apparent mass flowrates the liquid and gas phases of the multi-phasefluid may be determined as discussed below. Following the above example,the multi-phase fluid includes two liquid phases (for example, a firstliquid that is water and a second liquid that is a condensate) and a gasphase. However, similar calculations may be performed for othermulti-phase fluids. The apparent mass flowrates for the liquid mixture,and constituent liquid components, may be calculated using thefollowing:

m_(l) ^(a)=ρ_(l)ν_(l) ^(a)

m_(l1) ^(a)=ρ_(l1)ν_(l1) ^(a)

m_(l2) ^(a)=ρ_(l2)ν_(l2) ^(a)

where ν_(l) ^(a) is the apparent volumetric flowrate of the liquidmixture, ν_(l1) ^(a) is the apparent volumetric flowrate of the firstliquid, and ν_(l2) ^(a) is the apparent volumetric flowrate of thesecond liquid, all of which may be calculated as follows:

$v_{l}^{a} = {\frac{L\; V\; F^{2}}{100} \cdot v_{m}^{a}}$$v_{l\; 1}^{a} = {\frac{x_{l}}{100} \cdot v_{l}^{a}}$$v_{l\; 2}^{a} = {{\left( {1 - \frac{x_{l}}{100}} \right) \cdot v_{l}^{a}} = {v_{l}^{a} - {v_{l\; 1}^{a}.}}}$

The apparent volumetric flowrate of the multi-phase fluid, ν_(m) ^(a),may be calculated as follows:

$v_{m}^{a} = {\frac{m_{m}^{a}}{\rho_{m}^{a}}.}$

The apparent liquid volume fraction LVF^(a) may be calculated asfollows:

${{L\; V\; F^{a}} = {{{\frac{\rho_{m}^{a} - \rho_{g}}{\rho_{l} - \rho_{g}} \cdot 100}\%} = {100 - {G\; V\; F^{a}}}}},$

with the apparent gas void fraction, GVF^(a), being calculated based onthe following:

${G\; V\; F^{a}} = {{\frac{\rho_{l} - \rho_{m}^{a}}{\rho_{l} - \rho_{g}} \cdot 100}{\%.}}$

The apparent mass flowrate for the gas phase may be calculated using thefollowing:

{dot over (m)}_(g) ^(a)=ρ_(g)·ν_(g) ^(a)=ρ_(g0) ·sν _(g) ^(a),

where the apparent volumetric flowrate of the gas, ν_(g) ^(a), iscalculated using:

$v_{g}^{a} = {\frac{G\; V\; F^{a}}{100} \cdot {v_{m}^{a}.}}$

A measure of wetness (e.g., a Lockhart-Martinelli parameter) isdetermined based on a mapping between the one or more of the apparentintermediate values and the measure of wetness (525). In oneimplementation, the one or more intermediate values are the non-gasFroude number and the gas Froude number discussed above.

The mapping may be a neural network, a statistical model, a polynomial,a function, or any other type of mapping. The neural network or othermapping may be trained with data obtained from a multi-phase fluid forwhich values of the constituent phases are known in one implementation,prior to inputting an apparent intermediate value into the mapping, theapparent intermediate value may be filtered or conditioned to reducemeasurement and process noise. For example, linear filters may beapplied to the apparent intermediate value to reduce measurement noise.The time constant of the linear filter may be set to a value thatreflects the response time of the measurement instrumentation (e.g., 1second) such that the filter remains sensitive to actual changes in thefluid flowing through the flowtube (such as slugs of non-gas fluid)while also being able to reduce measurement noise.

The development of a mapping for correcting or improving a multiphasemeasurement may involve the collection of data under experimentalconditions, where the true or reference measurements are provided byadditional calibrated instrumentation. Generally, it is not practical tocarry out experiments covering all conceivable multi-phase conditions,either due to limitations of the test facility, and/or the cost and timeassociated with carrying out possibly thousands of experiments.Additionally, it is rarely possible to maintain multiphase flowconditions exactly constant for any extended period of time, due to theinherently unstable flow conditions that occur within multiphaseconditions. Accordingly, it is usually necessary to calculate theaverage values of all relevant parameters, including apparent and trueor reference parameter values, over the duration of each experiment,which may typically be of 30 s to 120 s duration. Thus, the mapping maybe constructed from experimental data where each data point is derivedfrom the average of for example 30 s to 120 s duration of data.

Difficulties might arise when applying the resulting mapping in themeter during multiphase flow in real time, whereby the particularparameter values observed within the meter are not included in themapping provided from the previously collected experimental data. Thereare two primary ways in which this may occur. In the first instance,although the conditions experienced by the meter, averaged over atimescale of about 15 to 120 seconds, do correspond to conditionscovered by the mapping, the instantaneous parameter values may falloutside of the region, due to measurement noise and or instantaneousvariations in actual conditions due to the instabilities inherent inmultiphase flow. As described above, this effect can to some extent bereduced by time-averaging or filtering the parameters used as inputsinto the mapping function, though there is a tradeoff between the noisereduction effects of such filtering and the responsiveness of the meterto actual changes in conditions within the multiphase flow.Alternatively, averaged parameter values may fall outside of the mappingbecause, for instance, it has not been economically viable to cover allpossible multiphase conditions during the experimental stage.

It may not be beneficial to apply a mapping function (whether neuralnet, polynomial or other function) to data that falls outside of theregion for which the mapping was intended. Application of the mapping tosuch data may result in poor quality measurements being generated.Accordingly, jacketing procedures may be applied to ensure that thebehavior of the mapping procedure is appropriate for parameter valuesoutside the mapped region, irrespective of the reasons for theparameters falling outside the mapped region. Data that is included inthe region may be referred to as suitable data.

Thus, the apparent intermediate value may be “jacketed” prior toinputting the apparent intermediate value into the mapping. Forimplementations that include one input to the mapping, the region ofsuitable data may be defined by one or more limits, a range, or athreshold. In other implementations, there may be more than one input tothe mapping. In these implementations, the region of suitable data maybe defined by a series of lines or planes. Accordingly, as the number ofinputs to the mapping increases, defining the region of suitable databecomes more complex. Thus, it may be desirable to use fewer inputs tothe mapping. The gas and non-gas Froude numbers described above are anexample of apparent intermediate values that may be input into themapping without additional inputs. Thus, use of the gas and non-gasFroude numbers may help to reduce the number of inputs into the mapping,which also may help reduce the complexity of the jacketing process.Additionally, using fewer inputs to the mapping may result in a simplermapping, which may help reduce the computational resources used by themapping and help increase the speed of determining correctedintermediate values based on the mapping.

Referring briefly to FIG. 7, an illustration of jacketing is shown. Inthis example, an apparent intermediate value 710 has a value that isoutside of the defined region 715 may be determined to be unsuitable forinput to the mapping. In this example, the region 715 is defined by twolines, line 720 and line 725. In general, rules are defined to correctan apparent intermediate value that is determined to be outside of thedefined region. For example, an apparent intermediate value that isoutside of the defined region (such as the apparent intermediate value710) may be ignored by the mapping (e.g., the apparent intermediatevalue is not corrected by the mapping), the apparent intermediate valuemay not be input to the mapping at all, a fixed correction may beapplied to the apparent intermediate value rather than a correctiondetermined by the mapping, or the correction corresponding to thecorrection that would apply to the value closest to the apparentintermediate value may be applied. Other rules for correcting anapparent intermediate value that is outside of the defined region may beimplemented. In general, the jacketing is specific to a particularmapping and is defined for each mapping.

Returning to FIG. 5A, the output of the mapping is a measure of wetnessat the flowtube. The measure of wetness generally provides an indicationof the amount of liquid present in the multi-phase fluid. Thus, in theexample process 500A, the Coriolis meter may act as an instrument thatprovides such a measure of wetness for the multi-phase fluid even thoughthe Coriolis meter is generally calibrated to measure properties of asingle-phase fluid. As discussed above, the measure of wetness may be aLockhart-Martinelli parameter.

Referring to FIG. 5B, an example process 500B may use the measure ofwetness and measurements made by differential flowmeter 304 to determineone or more phase-specific properties of a multi-phase process fluid.For example, the process 500B may be used to determine the mass flowrateof each phase of the multi-phase process fluid. In general, the exampleprocess 500B uses the measure of wetness of the multi-phase processfluid determined at the flowtube as described above (525) together witha second apparent property of the multi-phase process fluid measured bythe differential pressure flowmeter 304.

A multi-phase process fluid is passed through the differential pressureflowmeter 304 (560) and a second apparent property is determined usingthe differential pressure flowmeter 304 (565). The differential pressureflowmeter may be an orifice plate, as described above with respect toFIG. 3. In other implementations, the differential pressure flowmetermay be a Venturi flowmeter or a V-cone flowmeter. In still otherimplementations, any obstruction to the flow whose characteristics canbe determined may be used. Additionally or alternatively, other types offlowmeters may be used. For example, flowmeters based on vortex,turbine, electromagnetic, or ultrasonic phenomena may be used.

The second apparent property is an apparent property of the multi-phaseprocess fluid determined by the differential pressure flowmeter. In oneimplementation, the second apparent property is the mass flowrate of themulti-phase fluid determined by an orifice plate as if the fluid were adry gas. Like the Coriolis meter, the differential pressure flowmeterwill also produce inaccurate results when a multi-phase process fluid ispresent. In particular, a transmitter, or other processing device, usedto make determinations based on information received from a flowmeterthat includes an orifice plate may make determinations on the assumptionthat the multi-phase fluid is a dry gas. Thus, the readings from theorifice plate for a multi-phase fluid are inaccurate and generallyrepresent the mass flowrate of the multi-phase fluid as if it were a drygas.

One or more corrected phase-specific properties of the multi-phase fluidare determined based on the second apparent property and the measure ofwetness (570). In general, the multi-phase process fluid is themulti-phase process fluid that passed through the flowtube describedabove in FIG. 5A, though the multi-phase process fluid may undergophysical changes as the fluid flows between the flowtube and thedifferential pressure meter. For example, the temperature or pressure ofthe multi-phase process fluid may be different at the Coriolis meter andthe differential pressure flowmeter, and the density of the multi-phasefluid may be different at the flowtube and the Coriolis meter. Forexample, pressure and temperature changes may have a significant effecton any gas phases included in the multi-phase fluid. Accordingly, themeasure of wetness determined at the flowtube is transformed to ameasure of wetness at the differential pressure meter to account for thechanged conditions.

For example, if the measure of wetness is a Lockhart-Martinelliparameter, as described with respect to FIG. 5A, and the differentialpressure flowmeter is an orifice plate, the Lockhart-Martinelliparameter at the orifice plate may be expressed as follows, whereX_(L-M)(OP) is the Lockhart-Martinelli parameter at the orifice plate,X_(L-M)(FT) is the Lockhart-Martinelli parameter at the flowtube,p_(g)(OP) is the density of the gas phase of the multi-phase processfluid at the orifice plate, p_(l)(OP) is the density of the liquid phaseof the multi-phase process fluid at the orifice plate, p_(g)(FT) is thedensity of the gas phase of the multi-phase process fluid at theflowtube, and p_(l)(FT) is the density of the liquid phase of themulti-phase process fluid at the flowtube:

$\begin{matrix}{{X_{L - M}\left( {O\; P} \right)} = {\frac{m_{l}}{m_{g}}\sqrt{\frac{\rho_{g}\left( {O\; P} \right)}{\rho_{l}\left( {O\; P} \right)}}}} \\{= {{X_{L - M}\left( {F\; T} \right)} \cdot \sqrt{\frac{\rho_{l}\left( {F\; T} \right)}{\rho_{g}\left( {F\; T} \right)}} \cdot {\sqrt{\frac{\rho_{g}\left( {O\; P} \right)}{\rho_{l}\left( {O\; P} \right)}}.}}}\end{matrix}$

The estimated densities of the gas and liquid phases can be determinedin a manner similar to the manner described with respect to operation520 of process 500A, except for using the temperature and pressureconditions at the differential pressure flowmeter 304 rather than thoseconditions at the Coriolis flowmeter 306.

Continuing this example, one or more corrected phase-specific propertiesof the multi-phase process fluid are determined based on the massflowrate of the multi-phase fluid as a dry gas and theLockhart-Martinelli parameter at the orifice plate 304 (which is basedon the Lockhart-Martinelli parameter at the Coriolis flowmeter 306, asdescribed above). In this example, the phase-specific property is themass flowrate of the gas and liquid phases of the multi-phase processfluid. However, a similar process may be used to determine otherphase-specific properties for gas, liquid, and/or solid phases includedin a multi-phase process fluid.

In particular, the corrected mass flowrate of the gas phase of themulti-phase process fluid is determined based on the Lockhart-Martinelliparameter at the orifice plate (or other differential pressureflowmeter) according to the Murdock or other appropriate correctionequation (e.g., De Lecuw equations may be used for Venturi meters),where m_(gTP) is the mass flowrate of the multi-phase process fluid as adry gas, as measured by the differential pressure flowmeter, and X_(L-M)is the Lockhart-Martinelli parameter at the orifice plate:

$m_{g}^{c} = {\frac{m_{gTP}}{1 + {1.26X_{L - M}}}.}$

The mass flowrate of the liquid phase of the multi-phase process fluidmay be estimated based on the following equation:

$m_{l}^{c} = {X_{L - M}^{c} \cdot m_{g}^{c} \cdot {\sqrt{\frac{\rho_{l}}{\rho_{g}}}.}}$

When more than one liquid is included in the liquid phase, the massflowrates of the specific liquid components may be determined using thefollowing:

m_(i1) ^(c)=ρ_(l1)ν_(l1) ^(c)

m_(l2) ^(c)=ρ_(l2)ν_(l2) ^(c)

where ν_(l1) ^(c) is the corrected volumetric flowrate of the firstliquid, and ν_(l2) ^(c) is the corrected volumetric flowrate of thesecond liquid, all of which may be calculated as follows:

$v_{l}^{c} = \frac{m_{l}^{c}}{\rho_{l}}$$v_{l\; 1}^{c} = {\frac{x_{1}}{100} \cdot v_{l}^{c}}$$v_{l\; 2}^{c} = {\left( {1 - \frac{x_{1}}{100}} \right) \cdot v_{l}^{c}}$

Where x₁ is the known measured or assumed volumetric flow fraction offluid component 1 as before.

The Murdock correction is further described in Murdock, J. W.,“Two-phase flow with orifices,” Journal of Basic Engineering, ASMETransactions 84 (4), pp 419-433, December 1962.

As an alternative, particularly when the fluid is a wet gas, thecorrected mass flowrate of the gas phase may be determined from theChisholm correction equations below:

$m_{g} = {\frac{m_{gTP}}{\sqrt{1 + {C.X_{L - M}} + X_{L - M}^{2}}} = \frac{m_{gTP}}{\sqrt{1 + {X_{L - M} \cdot \left( {C.{+ X_{L - M}}} \right)}}}}$where$C = {\left( \frac{\rho_{l}}{\rho_{g}} \right)^{0.25} + {\left( \frac{\rho_{g}}{\rho_{l}} \right)^{0.25}\mspace{14mu} {\left( {{{for}\mspace{14mu} X_{L - M}} < 1} \right).}}}$

Additionally, the corrected mass flowrate of the liquid phases may bedetermined based on the following equations, which are described above:

m_(l 1)^(c) = ρ_(l 1)v_(l 1)^(c)m_(l 2)^(c) = ρ_(l 2)v_(l 2)^(c)$v_{l}^{c} = \frac{m_{l}^{c}}{\rho_{l}}$$v_{l\; 1}^{c} = {\frac{x_{1}}{100} \cdot v_{l}^{c}}$$v_{l\; 2}^{c} = {\left( {1 - \frac{x_{1}}{100}} \right) \cdot {v_{l}^{c}.}}$

The Chisholm correction is described further in Chisholm, D., “Flow ofincompressible two-phase mixtures through sharp-edged orifices,” IMechEJournal of Mechanical Engineering Science, Volume 9, No. 1, pp. 72-78,February 1967 and Chisholm, D., “Research Note: Two-phase flow throughsharp-edged orifices,” IMechE Journal of Mechanical Engineering Science,Volume 19, No. 3, pp. 128-130, June 1977.

In other implementations, other corrections may be used as appropriatedepending on the type of differential pressure flowmeter used. Forinstance, if a Venturi flowmeter is used, then the De Leeuw correctionmay be used. This correction is similar in form to the Chisholmcorrection with modified coefficients. See, for example, De Leeuw, H.,“Wet Gas Flow Measurement using a combination of Venturi meter and atracer technique,” North Sea Flow Measurement Workshop, Peebles,Scotland, October 1994 and De Leeuw, H., “Liquid Correction of VenturiMeter Readings in Wet Gas Flow,” North Sea Flow Measurement Workshop,Norway, October 1997.

Accordingly, a measure of wetness of a multi-phase process fluid passedthrough a flowtube may be used with an apparent property of themulti-phase process fluid determined by passing the fluid through adifferential pressure flowmeter to determine phase-specific propertiesof the multi-phase fluid.

Referring to FIG. 6, an example process 600 may be used for error orfault checking by comparing estimates of phase-specific propertiesdetermined by a Coriolis flowmeter to the corrected phase-specificproperties determined in process 500B. Consistency among thephase-specific properties determined in the two different ways mayprovide an indication that the Coriolis meter and the differentialpressure meter are operating properly.

As described with respect to FIGS. 5A and 5B, a Coriolis meter and adifferential pressure flowmeter may be used to determine phase-specificproperties, such as mass flowrate, for the constituent phases of amulti-phase process fluid. Using a process such as the process 600,phase-specific properties of the multi-phase process fluid also may bedetermined by the Coriolis meter alone, and these phase-specificproperties may be compared to those determined using the differentialpressure flowmeter. In general, if the Coriolis flowmeter and thedifferential pressure flowmeter are both operating properly, thephase-specific properties are similar regardless of the instruments usedto determine the properties.

One or more apparent intermediate values associated with the multi-phaseprocess fluid are determined based on a first apparent property (605).The first apparent property is the first apparent property discussedabove with respect to FIG. 5A. The apparent intermediate value may be,for example, a volume fraction of the multi-phase process fluid. Thevolume fraction may be a liquid volume fraction that specifies theportion of the multi-phase fluid that is a non-gas. The volume fractionalso may be a gas volume fraction that specifies the portion of themulti-phase fluid that is a gas. In general, the volume fraction is adimensionless quantity that may be expressed as a percentage. The gasvolume fraction also may be referred to as a void fraction. If themulti-phase fluid includes liquids and gases, the liquid and gas volumefractions add up to 100%. In other implementations, the apparentintermediate values may be a volumetric flowrate of the multi-phasefluid.

In one implementation, the apparent intermediate values are the apparentvolumetric flowrate and the apparent liquid volume fraction and aredetermined based on the apparent bulk mass flowrate and the apparentbulk density. The apparent volumetric flowrate in m³/s may be determinedfrom the following equation:

$v_{m}^{a} = {\frac{m_{m}^{a}}{\rho_{m}^{a}}.}$

The apparent liquid volume fraction, which is expressed as a percentage,may be determined from the following equation, where ρ_(l) is theestimated density of the liquid phase of the multi-phase process fluid,and ρ_(g) is the estimated density of the gas phase of the multi-phaseprocess fluid:

${L\; V\; F^{a}} = {{{\frac{\rho_{m}^{a} - \rho_{g}}{\rho_{l} - \rho_{g}} \cdot 100}\%} = {100 - {G\; V\; {F^{a}.}}}}$

The estimates of the liquid and gas densities may be obtained asdescribed above with respect to operation 520.

One or more corrected intermediate values are determined based on amapping between one or more apparent intermediate values and thecorrected intermediate values (610). For example, the correctedintermediate value may be a corrected liquid volume fraction, LVF^(c)(%), and/or a corrected volumetric flow, ν_(m) ^(c), m³/s. In oneparticular implementation, the corrected intermediate values are acorrected liquid volume fraction and a corrected volumetric flowratethat are corrected from the apparent liquid volume fraction and theapparent volumetric flowrate.

The mapping may be a neural network, a polynomial, a function, or anyother type of mapping that relates the apparent intermediate values andthe corrected intermediate values. In general, the mapping between theone or more apparent intermediate values and the corrected intermediatevalues is a different mapping than the mapping between the one or moreapparent intermediate values and the measure of wetness discussed abovewith respect to FIG. 5A. As discussed above, the inputs to the mappingmay be jacketed and or filtered. However, in some implementations, themappings may be the same.

The neural network or other mapping may be trained with data obtainedfrom a multi-phase fluid for which values of the constituent phases areknown. In one implementation, the mapping is a neural network that takesas inputs the apparent liquid volume fraction, the apparent volumetricflowrate, the pressure at the inlet of the vibratable flowtube, and thedifferential pressure across the vibratable flowtube. The neural networkproduces a corrected liquid volume fraction and a corrected mixturevolumetric flowrate.

One or more phase-specific properties of the multi-phase process fluidare determined based on the corrected intermediate value (615). Thephase-specific property maybe, for example, a mass flowrate and/or adensity of the non-gas and gas phases of the multi-phase fluid. Thefollowing equations illustrate the determination of the estimatedphase-specific mass flowrates of the constituent phases of themulti-phase process fluid based on the corrected mixture volumetricflowrate and the corrected liquid volume fraction.

The corrected volume fraction of the gas phase, GVF^(c) expressed as apercentage, may be determined from:

GVF ^(c)=100−LVF ^(c) %.

The phase-specific volumetric flowrate of the gas phase in m³/s maybedetermined from the following, where ν_(m) ^(c) is the corrected mixturevolumetric flow as discussed above with respect to (525):

ν_(g) ^(c) =GVF ^(c)·ν_(m) ^(c).

The phase-specific mass flowrate of the gas phase of the multi-phaseprocess fluid may be determined from the following equation:

m _(g) ^(c)=ρ_(g)·ν_(g) ^(c)=ρ_(g0) ·sv _(g) ^(c),

where the corrected standard volumetric flow sv_(g) ^(c), of the gas atdefined standard conditions of temperature and pressure where it hasdensity ρ_(g0) is given by

${sv}_{g}^{c} = {\frac{\rho_{g}}{\rho_{g\; 0}}{v_{g}^{c}.}}$

The phase-specific mass flowrate also may be determined for the non-gasphases of the multi-phase process fluid (both the liquid mixture andspecific liquid components). Continuing the example above, themulti-phase process fluid has a gas phase and two liquid phases. Thecorrected volumetric flowrates (m³/s) of the liquid mixture and thespecific liquid phases may be determined from the following equation,where v_(m) ^(c) is the corrected volumetric flowrate as discussedabove:

$v_{l}^{c} = {\frac{L\; V\; F^{c}}{100} \cdot v_{m}^{c}}$$v_{l\; 1}^{c} = {{{\frac{x_{1}}{100} \cdot v_{l}^{c}}v_{l\; 2}^{c}} = {{\left( {1 - \frac{x_{1}}{100}} \right) \cdot v_{l}^{c}} = {v_{l}^{c} - {v_{l\; 1}^{c}.}}}}$

The phase-specific mass flowrate of the first and second liquid phases(and the liquid mass flowrate) may then be determined from the followingequations:

m_(l) ^(c)=ρ_(l)ν_(l) ^(c)

m_(l1) ^(c)=ρ_(l1)ν_(l1) ^(c)

m_(l2) ^(c)=ρ_(l2)ν_(l2) ^(c)

The estimated phase-specific properties determined based on thecorrected intermediate value in (615) are compared to the correctedphase-specific property based on the measure of wetness and the secondapparent property (620). Comparing the estimated phase-specificproperties, which are determined based on data from a Coriolis meter, tothe corrected phase-specific properties, which are determined based ondata from a Coriolis meter and a differential pressure meter, allows anassessment of whether the instruments are performing properly. Forexample, if the phase-specific properties are compared and found to besimilar, it is generally an indication that the Coriolis meter and thedifferential pressure meter are performing properly.

The calculations described in the various implementations may beperformed by the transmitter of the Coriolis flowmeter, by a computingdevice coupled to the Coriolis meter and/or the differential pressureflowmeter, or by a flow computer or computing device coupled to theCoriolis flowmeter and the differential pressure flowmeter.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made. Accordingly, otherimplementations are within the scope of the following claims.

1. A method comprising: passing a multi-phase process fluid through avibratable flowtube and a differential pressure flowmeter; inducingmotion in the vibratable flowtube; determining a first apparent propertyof the multi-phase process fluid based on the motion of the vibratableflowtube; determining one or more apparent intermediate valuesassociated with the multi-phase process fluid based on the firstapparent property; determining a measure of wetness of the multi-phaseprocess fluid based on a mapping between one or more of the apparentintermediate values and the measure of wetness; determining a secondapparent property of the multi-phase process fluid using thedifferential pressure flowmeter; and determining one or morephase-specific properties of the multi-phase process fluid based on themeasure of wetness and the second apparent property.
 2. The method ofclaim 1, wherein: determining one or more apparent intermediate valuesassociated with the multi-phase process fluid based on the firstapparent property includes determining a first Froude numbercorresponding to a non-gas phase of the multi-phase process fluid and asecond Froude number corresponding to a gas phase of the multi-phaseprocess fluid; and determining the measure of wetness of the multi-phaseprocess fluid based on a mapping between one or more of the apparentintermediate values and the measure of wetness includes determining themeasure of wetness of the multi-phase process fluid based on a mappingbetween the first and second Froude numbers and the measure of wetness.3. The method of claim 1, wherein the multi-phase process fluid is a wetgas.
 4. The method of claim 1, wherein the first apparent property is anapparent mass flow rate.
 5. The method of claim 1, wherein the measureof wetness is a Lockhart-Martinelli parameter.
 6. The method of claim 1,wherein the differential pressure flowmeter is an orifice plate.
 7. Themethod of claim 1, wherein the second apparent property is a mass flowrate of the multi-phase process fluid as a dry gas.
 8. The method ofclaim 1, further comprising: determining one or more correctedintermediate values based on a mapping between one or more of theapparent intermediate values and the corrected intermediate valuesdetermining one or more phase-specific properties of the multi-phasefluid based on the corrected intermediate values; and comparing thephase-specific properties of the phase of the multi-phase fluiddetermined based on the corrected intermediate value to thephase-specific properties of the multi-phase process fluid determinedbased on the measure of wetness and the second apparent property.
 9. Themethod of claim 1, wherein determining one or more phase-specificproperties of the multi-phase process fluid based on the measure ofwetness and the second apparent property includes determining a massflow rate of a gas phase of the multi-phase process fluid.
 10. Themethod of claim 1, wherein the mapping is a neural network.
 11. Aflowmeter comprising: a vibratable flowtube, the flowtube beingconfigured to receive a multi-phase fluid; a driver connected to theflowtube and configured to impart motion to the flowtube such that theflowtube vibrates; a sensor connected to the flowtube and configured tosense the motion of the flowtube and generate a sensor signal; and acontroller to receive the sensor signal and configured to: determine afirst apparent property of the multi-phase process fluid based on themotion of the vibratable flowtube; determine one or more apparentintermediate values associated with the multi-phase process fluid basedon the first apparent property; determine a measure of wetness of themulti-phase process fluid based on a mapping between one or more of theapparent intermediate values and the measure of wetness; receive asecond apparent property of the multi-phase process fluid, the secondapparent property being determined using a differential pressureflowmeter; and determine one or more phase-specific properties of themulti-phase process fluid based on the measure of wetness and the secondapparent property.
 12. The flowmeter of claim 11, wherein: to determineone or more apparent intermediate values associated with the multi-phaseprocess fluid based on the first apparent property, the controller isconfigured to determine a first Froude number corresponding to a non-gasphase of the multi-phase process fluid and a second Froude numbercorresponding to a gas phase of the multi-phase process fluid; and todetermine the measure of wetness of the multi-phase process fluid basedon a mapping between one or more of the apparent intermediate values andthe measure of wetness, the controller is configured to determine themeasure of wetness of the multi-phase process fluid based on a mappingbetween the first and second Froude numbers and the measure of wetness.13. The flowmeter of claim 11, wherein the multi-phase process fluid isa wet gas.
 14. The flowmeter of claim 11, wherein the first apparentproperty is an apparent mass flow rate.
 15. The flowmeter of claim 11,wherein the measure of wetness is a Lockhart-Martinelli parameter. 16.The flowmeter of claim 11, wherein the differential pressure flowmeteris an orifice plate.
 17. The flowmeter of claim 11, wherein the secondapparent property is a mass flow rate of the multi-phase process fluidas a dry gas.
 18. The flowmeter of claim 11, wherein the controller isfurther configured to: determine one or more corrected intermediatevalues based on a mapping between one or more of the apparentintermediate values and the corrected intermediate values determine oneor more phase-specific properties of the multi-phase fluid based on thecorrected intermediate values; and compare the phase-specific propertiesof the phase of the multi-phase fluid determined based on the correctedintermediate value to the phase-specific properties of the multi-phaseprocess fluid determined based on the measure of wetness and the secondapparent property.
 19. The flowmeter of claim 11, wherein, to determineone or more phase-specific properties of the multi-phase process fluidbased on the measure of wetness and the second apparent property, thecontroller is configured to determine a mass flow rate of a gas phase ofthe multi-phase process fluid.
 20. A flowmeter transmitter for use witha vibratable flowtube coupled to a differential pressure flowmeter suchthat a multi-phase process fluid passes through the vibratable flowtubeand the differential pressure flowmeter, the flowmeter transmittercomprising: at least one processing device; and a storage device, thestorage device storing instructions for causing the at least oneprocessing device to: induce motion in the vibratable flowtube, thevibratable flowtube being configured to receive a multi-phase processfluid; determine a first apparent property of the multi-phase processfluid based on the motion of the vibratable flowtube; determine one ormore apparent intermediate values associated with the multi-phaseprocess fluid based on the first apparent property; determine a measureof wetness of the multi-phase process fluid based on a mapping betweenone or more of the apparent intermediate values and the measure ofwetness; receive a second apparent property of the multi-phase processfluid, the second apparent property being determined using adifferential pressure flowmeter; and determine one or morephase-specific properties of the multi-phase process fluid based on themeasure of wetness and the second apparent property.
 21. The transmitterof claim 20, wherein: to determine one or more apparent intermediatevalues associated with the multi-phase process fluid based on the firstapparent property, the instructions include instructions for causing theprocessing device to determine a first Froude number corresponding to anon-gas phase of the multi-phase process fluid and a second Froudenumber corresponding to a gas phase of the multi-phase process fluid;and to determine the measure of wetness of the multi-phase process fluidbased on a mapping between one or more of the apparent intermediatevalues and the measure of wetness, the instructions include instructionsfor causing the processing device to determine the measure of wetness ofthe multi-phase process fluid based on a mapping between the first andsecond Froude numbers and the measure of wetness.
 22. The transmitter ofclaim 20, wherein the multi-phase process fluid is a wet gas.
 23. Thetransmitter of claim 20, wherein the first apparent property is anapparent mass flow rate.
 24. The transmitter of claim 20, wherein themeasure of wetness is a Lockhart-Martinelli parameter.
 25. Thetransmitter of claim 20, wherein the to determine one or morephase-specific properties of the multi-phase process fluid based on themeasure of wetness and the second apparent property, the instructionsinclude instructions for causing the processing device to determine amass flow rate of a gas phase of the multi-phase process fluid.
 26. Asystem comprising: a vibratable flowtube configured to receive amulti-phase process fluid; a differential pressure flowmeter coupled tothe vibratable flowtube; and one or more processing devices configuredto: induce motion in the vibratable flowtube; determine a first apparentproperty of the multi-phase process fluid based on the motion of thevibratable flowtube; determine one or more apparent intermediate valuesassociated with the multi-phase process fluid based on the firstapparent property; determine a measure of wetness of the multi-phaseprocess fluid based on a mapping between one or more of the apparentintermediate values and the measure of wetness; receive a secondapparent property of the multi-phase process fluid determined using thedifferential pressure flowmeter; and determine one or morephase-specific properties of the multi-phase process fluid based on themeasure of wetness and the second apparent property.
 27. The system ofclaim 26, wherein: to determine one or more apparent intermediate valuesassociated with the multi-phase process fluid based on the firstapparent property, the one or more processing devices are configured todetermine a first Froude number corresponding to a non-gas phase of themulti-phase process fluid and a second Froude number corresponding to agas phase of the multi-phase process fluid; and to determine the measureof wetness of the multi-phase process fluid based on a mapping betweenone or more of the apparent intermediate values and the measure ofwetness, the one or more processing devices are configured to determinethe measure of wetness of the multi-phase process fluid based on amapping between the first and second Froude numbers and the measure ofwetness.
 28. The system of claim 26, wherein the one or more processingdevices are further configured to: determine one or more correctedintermediate values based on a mapping between one or more of theapparent intermediate values and the corrected intermediate valuesdetermine one or more phase-specific properties of the multi-phase fluidbased on the corrected intermediate values; and compare thephase-specific properties of the phase of the multi-phase fluiddetermined based on the corrected intermediate value to thephase-specific properties of the multi-phase process fluid determinedbased on the measure of wetness and the second apparent property. 29.The system of claim 26, wherein the first apparent property comprises anapparent mass flow rate, and the second apparent property comprises amass flow rate of the multi-phase process fluid as a dry gas.
 30. Thesystem of claim 26, wherein to determine one or more phase-specificproperties of the multi-phase process fluid based on the measure ofwetness and the second apparent property, the one or more processingdevices are configured to determine a mass flow rate of a gas phase ofthe multi-phase process fluid.